# Fluctuations of Brownian motion with drift

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Publisher
Universitat Autònoma de Barcelona: Servei de Publicacions
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Keywords
• Proceso De Difusión
• Ecuaciones Diferenciales Estocásticas
• Procesos Estocásticos
• Movimiento Browniano

## Abstract

Consider 3 dimensional Brownian motion started on the unit sphere $\{|x|=1\}$ with initial density $\rho$. Let $\rho_t$ be the first hitting density on the sphere $\{|x|=t+1\}$, $t>0$. Then the linear operators $T_t$ defined by $T_t$ $\rho=\rho_t$ form a semigroup with an infinitesimal generator which is approximately the square root of the Laplacian. This paper studies the analogous situation for Brownian motion with a drift $\bold b$, where $\bold b$ is small in a suitable scale invariant norm

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